Degenerate parabolic equations in divergence form: fundamental solution and Gaussian bounds
Abstract
Abstract In this paper, we consider second-order degenerate parabolic equations with complex, measurable, and time-dependent coefficients. The degenerate ellipticity is dictated by a spatial $$A_2$$ A 2 -weight. We prove that having a generalized fundamental solution with upper Gaussian bounds is equivalent to Moser’s $$L^2$$ L 2 - $$L^\infty $$ L ∞ estimates for local weak solutions. In the special case of real coefficients, Moser’s $$L^2$$ L 2 - $$L^\infty $$ L ∞ estimates are known, which provide an easier proof of Gaussian upper bounds, and a known Harnack inequality is then used to derive Gaussian lower bounds.
Fields of Study & Subjects
Differential Equations and Boundary Problems
Publication details
- Journal / source
- Journal of Evolution Equations
- Publisher
- Springer Science and Business Media LLC
- Volume
- 26
- Issue
- 2
- Publication date
- 31 March 2026
- Language
- EN